Answer:[tex]k=\frac{1}{2}[/tex]Step-by-step explanation:The given rational equation is [tex]\frac{5k}{k+2}+\frac{2}{k}=5[/tex]The Least Common Denominator is [tex]k(k+2)[/tex]Multiply each term by the LCD.[tex]k(k+2)\times \frac{5k}{k+2}+k(k+2)\times \frac{2}{k}=5k(k+2)[/tex]Simplify;[tex]k\times \frac{5k}{1}+(k+2)\times \frac{2}{1}=5k(k+2)[/tex][tex]\Rightarrow k(5k)+2(k+2)=5k(k+2)[/tex]Expand;[tex]\Rightarrow 5k^2+2k+4=5k^2+10k[/tex]Group similar terms;[tex]\Rightarrow 5k^2-5k^2+2k-10k=-4[/tex][tex]\Rightarrow -8k=-4[/tex]Divide by -8.[tex]k=\frac{1}{2}[/tex]